Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3811)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=1, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=1, b₁=11/2

http://functions.wolfram.com/07.25.03.3811.01

Input Form

HypergeometricPFQ[{-(9/2), 1}, {11/2, 6}, z] == (45 (168 - 3192 z + 9044 z^2 - 9044 z^3 + 4199 z^4))/(46189 z^5) + (1/(567570432 z^5)) (E^z (-92897280 + 1203216525 z - 2447606700 z^2 + 1821037680 z^3 - 643397040 z^4 + 120984864 z^5 - 12667200 z^6 + 733440 z^7 - 21760 z^8 + 256 z^9)) + (1/(1135140864 z^(9/2))) (Sqrt[Pi] (654729075 - 3928374450 z + 6285399120 z^2 - 4190266080 z^3 + 1396755360 z^4 - 253955520 z^5 + 26046720 z^6 - 1488384 z^7 + 43776 z^8 - 512 z^9) Erfi[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]